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### Factorials of Negative Integers

```Date: 06/27/2002 at 02:21:04
From: Steven
Subject: factorial

Is it possible to compute the factorial of a negative number, e.g.,

(-4)! = ?
```

```
Date: 06/28/2002 at 05:33:31
From: Doctor Floor
Subject: Re: factorial

Hi, Steven,

Starting from the explanation for 0! in the Dr. Math FAQ,

0! = 1
http://mathforum.org/dr.math/faq/faq.0factorial.html

if we try to extend this to -1, we find that (-1)! = 1/0 which means
that (-1!) is undefined. Extending further to (-2)! etc. is thus
impossible as well.

The same FAQ mentions the Gamma function, which generalizes the idea
of factorial to non-integer numbers.  Note that this function also
yields undefined values for negative integer factorials.

If you have more questions, just write back.

Best regards,

- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Factorials
Middle School Negative Numbers

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